Use of an altitude sensor to augment availability of GPS location fixes

Abstract

Methods for GPS-assisted determination of location coordinates of a mobile user or selected position on or adjacent to the Earth's surface with improved accuracy. Elevation readings from an altimeter or barometer are integrated with readings of the GPS-determined elevation coordinate for that location, using Kalman filter techniques, minimum least square techniques, or comparison of certain statistically defined parameters associated with the altimeter and GPS variables, such as the standard deviation of the expected errors in these variables. The resulting elevation coordinate may be a statistical blend or filtered blend of the altimeter value and a GPS-determined value for the elevation coordinate; or this resulting elevation coordinate can be chosen to be one or the other of these values, based upon comparison of time varying statistical parameters corresponding to the altimeter and the GPS.

We claim: 
     
       1. A method for determination of location coordinates of a selected three-dimensional location of a user on or adjacent to the Earth's surface, the method comprising the steps of: receiving Global Positioning System (GPS) signals from at least three GPS satellites, numbered i=1, 2, . . . , and measuring the pseudoranges ρ i  from satellite number i to a selected user location;   representing the pseudorange ρ i  at a selected measurement time t=t k  as a sum   ρ.sub.i (t.sub.k)=r.sub.i +b+e.sub.i,       r.sub.i =r.sub.i (t.sub.k)={(x.sub.i (t.sub.k)-x(t.sub.k)).sup.2 +(y.sub.i (t.sub.k)-y(t.sub.k)).sup.2 +(z.sub.i (t.sub.k)-z(t.sub.k)).sup.2 }.sup.1/2,     where (x i ,y i ,z i ) are the known, time varying location coordinates of the ith satellite in a selected first coordinate system, (x,y,z) are the true location coordinates of the user, to be determined, in the selected first coordinate system, b is an unknown user clock bias, and e i  represents other unknown measurement errors for satellite i, at the measurement time t=t k  ;     providing a nominal location solution set (x n ,y n ,z n ) of known location coordinates in the selected first coordinate system that provide a nominal estimate of location solutions for the pseudorange equations for the three satellites, and defining   r.sub.i,n (t.sub.k)={(x.sub.i (t.sub.k)-x.sub.n).sup.2 +(y.sub.i (t.sub.k)-y.sub.n).sup.2 +(z.sub.i (t.sub.k)-z.sub.n).sup.2 }.sup.1/2,       ρ.sub.i,n (t.sub.k)=r.sub.i,n (t.sub.k)+e.sub.i ' (i=1,2,3)     where e i  ' is an estimate of the variable e i  ;     computing pseudorange increments δρ i ,n =ρ i  -ρ i ,n, for the three satellites numbered i=1, 2, 3;   selecting a triple of location coordinates (x 4 , y 4 , z 4 )=(0,0,0) for a fictitious fourth satellite, numbered i=4, in the selected first coordinate system, where the distance from the fourth satellite location to the nominal solution location (x n ,y n ,z n ) is   r.sub.4,n =r.sub.n ={(x.sub.n).sup.2 +(y.sub.n).sup.2 +(z.sub.n).sup.2 }.sup.1/2 ;       providing a selected mean sea level surface S ms1  that represents the average mean sea level of the Earth;   providing a selected ellipsoidal surface S ell  that approximates the surface of the Earth;   representing the scalar length   r={(x'.sup.2 +y'.sup.2 +z'.sup.2 }.sup.1/2     of a vector r extending from the fourth satellite location to a location with coordinates (x',y',z'), where an extension of the vector r intersects the surface S ell  and thereby defines a vector r ell  (x',y',z') from the fourth satellite to this intersection point, as a sum of the length r s  (x',y',z') of the vector r ell  plus the signed altitude A ell  of the user with respect to the selected ellipsoidal surface,     r=r.sub.s +A.sub.ell ;       providing an altitude sensor having an altimeter reading z alt  (t) as an estimate of an elevation coordinate A ms1  (t) of the user above the mean sea level surface at a selected time t, where z alt  (t) is a sum of terms including the elevation coordinate A ms1  (t), plus a bias term B(t) arising from altitude sensor measurement error, plus a sensor noise error term Q(t) that has approximately zero mean;   providing a reference elevation coordinate z ref  (t) as a sum including the elevation coordinate A ms1  (t) plus an error term G(t) that has approximately zero mean in the reference elevation coordinate at a selected calibration time t=t cal , where z ref  (t cal ) is determined using at least one of (i) the altitude A ms1  obtained from a GPS location solution, computed using at least four satellites with no altitude constraints at one or more selected times t=t cal , and (ii) an independently determined, accurate value of A ms1  (t cal );   computing an estimated altitude A est  (t) of the elevation coordinate A ms1  (t), from which the sensor bias has been removed, for a selected interval of times t>t cal  as a difference A est  (t)=z alt  (t)-C(t cal ), where C(t cal )=z alt  (t cal )-z ref  (t cal );   providing a selected second coordinate system that is expressed in latitude, longitude and altitude coordinates, (lat,lon,alt), where the altitude coordinate is A ell  ;   determining the latitude, longitude and altitude coordinates (lat n , lon n , alt n ) that correspond to the nominal solution location coordinate values (x n ,y n ,z n ) in the selected second coordinate system;   determining a signed distance ΔMSL(lat n ,lon n )=A ms1  -A ell  of the selected ellipsoidal surface above the mean sea level surface at a location whose latitude and longitude coordinates in the selected second coordinate system are (lat n , lon n ), from a look-up table that provides the signed difference between the height of the selected ellipsoid surface and the mean sea level surface at a location with latitude and longitude coordinates (lat,lon) and arbitrary altitude in the selected second coordinate system for a location with selected location coordinates in the selected first coordinate system;   expressing the length r s  (x n ,y n ,z n ) of the vector r ell  (x n ,y n ,z n ) as a sum ##EQU11## calculating a distance r 4  from the fourth satellite to a location at the altitude A est  by the relation   r 4  =r s  (x n ,y n ,z n )+(A est  -ΔMSL(x n ,y n ,z n )), using the estimated altitude A est , and forming a difference   
     
     
       δρ 4 . n =r 4  -r 4 ,n ; forming a 4×4 matrix H having entries H ik  (i=1, 2, 3, 4; k=1, 2, 3, 4) defined by H i1  =(x n  -x i )/r i ,n, H i2  =(y n  -y i )/r i ,n, H i3  =(z n  -z i )/r i ,n for i=1, 2, 3, H 41  =(x n )/r 4 ,n, H 42  =(y n )/r 4 ,n, H 43  =(z n )/r 4 ,n, H 14  =H 24  =H 34  =1, and H 44  =0, and computing an inverse matrix H -1  =G with entries G ik  ;   computing estimated location coordinate values (x p ,y p ,z p ) for the unknown location coordinates (x,y,z), defined by ##EQU12## using the estimated location coordinate values (x p ,y p ,z p ) to determine and display, by visually perceptible means or audibly perceptible means, an estimated present location of the user.   
     
     
       2. The method of claim 1, further comprising the step of converting said estimated location coordinate values (x p ,y p ,z p ) to said selected second coordinate system with the coordinate values (lat p ,lon p ,alt p ). 
     
     
       3. The method of claim 1, further comprising the steps of: choosing as said reference elevation coordinate z ref  (t) at said calibration time t=t cal  a trailhead value z tr  of said coordinate z ref  (t) that corresponds to a location site for which said altitude A ms1  is known; and   determining said estimated altitude coordinate A est  by A est  =A ms1  -ΔMSL(lat n ,lon n ) at said calibration time t=t cal .   
     
     
       4. The method of claim 1, further comprising the steps of: providing a user of said GPS with an independent estimate of relative altitude z alt  (t) for said altimeter; and   choosing, as said reference elevation coordinate z ref  (t=t cal ), a time average z gps ,avg of said GPS estimate z gps  (t) of said true elevation or vertical coordinate over an interval times t=t n  ≦t cal  (n=1, 2, . . . ) of a selected length T, during which at least one of four conditions occurs: (i) said GPS estimate z gps  (t) changes by no more than a selected threshold amount Δz gps ,thr, according to the independent estimate of relative altitude; (ii) the user determines that said true elevation z gps  (t) changes by no more than a selected threshold amount Δz gps ,thr ; (iii) the magnitude of the vertical component of velocity, |Δv vert ,gps |, estimated from GPS signals received from said GPS satellites, is no greater than a selected threshold Δv vert ,thr ; and (iv) the magnitude of the horizontal component of velocity, |Δv horiz ,gps |, estimated from GPS signals received from said GPS satellites, is no greater than a selected threshold Δv horiz ,thr.   
     
     
       5. The method of claim 1, wherein said step of providing a reference elevation coordinate z ref  (t) comprises the steps of: forming said difference between said altitude sensor reading and said reference elevation coordinate, C(t)=z alt  (t)-z ref  (t)=x +v1+v2, as a sum of a state vector x (t) representing the altitude sensor bias and two statistical variables v1(t)=Q(t) and v2(t)=-G(t) that are independent, are approximately normally distributed, and have approximately zero statistical means;   selecting an initial estimate x 0  - of the state vector x  at a selected initial time t=t 0  and an initial uncertainty vector P 0  - that is equal to a number much larger than 1;   for each of a sequence of at least two times t=t k  >t 0  (k=1, 2, . . . ), forming an altimeter bias term estimate C k  =C(t k ), a gain estimate K k , an updated state vector x k  and an estimate P k  of an error variance by the relations   K.sub.k =P.sub.k -/(P.sub.k - +R.sub.k),       x .sub.k =x .sub.k - +K.sub.k (C.sub.k -x .sub.k -)=(I-C.sub.k)x .sub.k - +K.sub.k C.sub.k,       P.sub.k =(I-K.sub.k)P.sub.k -;       computing a new estimate of the error variance   P.sub.k+1.sup.- =P.sub.k +D.sub.k,     where D k  is an estimate of the drift variance between two consecutive updates x hd k and x  k  of the state vector x;     identifying the value x  k  with an estimate of the altitude sensor bias B(t k ) at time t=t k  ; and   computing an estimate A est  (t cal ) for said true elevation coordinate at a selected location at a selected time t=t cal  ≈t k  by A est  (t cal )=z alt  (t cal )-x (t cal ).   
     
     
       6. The method of claim 1, further comprising the steps of: forming said difference between said readings of said altitude sensor and of said reference elevation coordinate, C(t)=z alt  (t)-z ref  (t)=B(t)+Q(t)-G(t), at each of a sequence of times t=t n  (n=1, 2, . . . );   computing a filtered value C f  (t) of said value C(t) at each of a sequence of times by the relation C f  (t n )=(1-K n ) C(t n-1 )+K n  z alt  (t n ), where K n  =max and N max  is a selected positive integer;   computing said estimated altitude coordinate value A est  (t) at each of the sequence of times t for which t≧t Nmax  as a difference A est  (t)=z alt  (t)-C f  (t n ); and   replacing said location solution coordinate z gps  (t) by the value A est  (t) for at least one time t>t cal .   
     
     
       7. A method for determination of location coordinates of a selected three-dimensional location of a user on or adjacent to the Earth's surface, the method comprising the steps of: receiving Global Positioning System (GPS) signals from at least three GPS satellites, numbered i=1, 2, 3, . . . , N-1 (N-1≧3) and measuring the pseudoranges ρ i  from satellite number i to a selected user location;   representing the pseudorange ρ i  at a selected measurement time t=t k  as a sum   ρ.sub.i (t.sub.k)=r.sub.i +b+e.sub.i,       r.sub.i =r.sub.i (t.sub.k)={(x.sub.i (t.sub.k)-x(t.sub.k)).sup.2 +(y.sub.i (t.sub.k)-y(t.sub.k)).sup.2 +(z.sub.i (t.sub.k)-z(t.sub.k)).sup.2 }.sup.1/2,     where (x i ,y i ,z i ) are the known, time varying location coordinates of the ith satellite in a selected first coordinate system, (x,y,z) are the true location coordinates of the user, to be determined, in the selected first coordinate system, b is an unknown user clock bias, and e i  represents other unknown measurement errors for satellite i, at the measurement time t=t k  ;     providing a nominal location solution set (x n ,y n ,z n ) of known location coordinates in the selected first coordinate system that provide a nominal estimate of location solutions for the pseudorange equations for the three satellites, and defining   r.sub.i,n (t.sub.k)={(x.sub.i (t.sub.k)-x.sub.n).sup.2 +(y.sub.i (t.sub.k)-y.sub.n).sup.2 +(z.sub.i (t.sub.k)-z.sub.n).sup.2 }.sup.1/2,       ρ.sub.i,n (t.sub.k)=r.sub.i,n (t.sub.k)+e.sub.i ' (i =1,2,3, . . . , N-1),     where e i  ' is an estimate of the variable e i  ;     computing pseudorange increments δρ i ,n =ρ i  -ρ i ,n, for the N-1 satellites numbered i=1, 2, . . . , N-1;   selecting a triple of location coordinates (x N ,y N ,z N )=(0,0,0) for a fictitious Nth satellite, numbered i=N, in the selected first coordinate system, where the distance from the fourth satellite location to the nominal solution location (x n ,y n ,z n ) is   r.sub.N,n =r.sub.n ={(x.sub.n).sup.2 +(y.sub.n).sup.2 +(z.sub.n).sup.2 }.sup.1/2 ;       providing a selected mean sea level surface S ms1  that represents the average mean sea level of the Earth;   providing a selected ellipsoid surface S ell  that approximates the surface of the Earth;   representing the scalar length   r={x'.sup.2 +y'.sup.2 +z'.sup.2 }.sup.1/2     of a vector r extending from the fourth satellite location to a location with coordinates (x',y',z'), where an extension of the vector r intersects the surface S ell  and thereby defines a vector r ell  (x',y',z') from the fourth satellite to this intersection point, as a sum of the length r s  (x',y',z') of the vector r ell  plus the signed altitude A ell  of the user with respect to the selected ellipsoidal surface,     r=r.sub.s +A.sub.ell ;       providing an altitude sensor having an altimeter reading z alt  (t) as an estimate of an elevation coordinate A ms1  (t) of the user above the mean sea level surface at a selected time t, where z alt  (t) is a sum of terms including the elevation coordinate A ms1  (t.sub.), plus a bias term B(t) arising from altitude sensor measurement error, plus a sensor noise error term Q(t) that has approximately zero mean;   providing a reference elevation coordinate z ref  (t) as a sum including the elevation coordinate A ms1  (t) plus an error term G(t) that has approximately zero mean in the reference elevation coordinate at a selected calibration time t=t cal , where z ref  (t cal ) is determined using at least one of (i) the altitude A ms1  obtained from a GPS location solution, computed using at least four satellites with no altitude constraints at one or more selected times t=t cal , and (ii) an independently determined, accurate value of A ms1  (t cal );   computing an estimated altitude A est  (t) of the elevation coordinate A ms1  (t), from which the sensor bias has been removed, for a selected interval of times t>t cal  as a difference A est  (t)=z alt  (t)-C(t cal ), where C(t cal )=z alt  (t cal )-z ref  (t cal );   providing a selected second coordinate system that is expressed in latitude, longitude and altitude coordinates, (lat,lon,alt), where the altitude coordinate is A ell  ;   determining the latitude, longitude and altitude coordinates (lat n , lon n , alt n ) that correspond to the nominal solution location coordinate values (x n ,y n ,z n ) in the selected second coordinate system;   determining a signed distance ΔMSL(lat n ,lon n )=A ms1  -A ell  of the selected ellipsoidal surface above the mean sea level surface at a location whose latitude and longitude coordinates in the selected second coordinate system are (lat n , lon n ), from a look-up table that provides the signed difference between the height of the selected ellipsoid surface and the mean sea level surface at a location with latitude and longitude coordinates (lat,lon) and arbitrary altitude in the selected second coordinate system for a location with selected location coordinates in the selected first coordinate system;   expressing the length r s  (x n ,y n ,z n ) of the vector r ell  (x n ,y n ,z n ) as a sum ##EQU13## calculating a distance r N  from the Nth satellite to a location at the altitude A est  by the relation   r.sub.N =r.sub.s (x.sub.n,y.sub.n,z.sub.n)+(A.sub.est -ΔMSL(x.sub.n,y.sub.n,z.sub.n)),     using the estimated altitude A est , and forming a difference     
     
     
       δρ 4 . n =r N  -r N ,n ; forming an N×4 matrix H having entries H ik  (i=1, 2, 3, . . . , N; k=1, 2, 3, 4) defined by H i1  =(x n  -x i )/r i ,n, H i2  =(y n  -y i )/r i ,n, H i3  =(z n  -z i )/r i ,n for i=1, 2, 3, . . . N-1, H N1  =(x n )/r N ,n, H N2  =(y n )/r N ,n, H N3  =(z n )/r N ,n, H N4  =0, H 14  =H 24  =H 34  = . . . =H N-1 ,4 =1, and computing a 4×N matrix (H tr  H) -1  H tr  =G with entries G ik  ;   computing estimated location coordinate values (x p ,y p ,z p ) for the unknown location coordinates (x,y,z), defined by ##EQU14## using the estimated location coordinate values (x p ,y p ,z p ) to determine and display, by visually perceptible means or audibly perceptible means, an estimated present location of the user.   
     
     
       8. The method of claim 7, further comprising the step of converting said estimated location coordinate values (x p ,y p ,z p ) to said selected second coordinate system with the coordinate values (lat p ,lon p ,alt p ). 
     
     
       9. The method of claim 7, further comprising the steps of: choosing as said reference elevation coordinate z ref  (t) at said calibration time t=t cal  a trailhead value z tr  of said coordinate z ref  (t) that corresponds to a location site for which said altitude A ms1  is known; and determining said estimated altitude coordinate A est  by A est  =A ms1  -ΔMSL(lat n ,lon n ) at said calibration time t=t cal .   
     
     
       10. The method of claim 7, further comprising the steps of: providing a user of said GPS with an independent estimate of relative altitude z alt  (t) for said altimeter; and   choosing, as said reference elevation coordinate z ref  (t=t cal ), a time average z gps ,avg of said GPS estimate z gps  (t) of said true elevation or vertical coordinate over an interval times t=t n  ≦t cal  (n=1, 2, . . . ) of a selected length T, during which at least one of four conditions occurs: (i) said GPS estimate z gps  (t) changes by no more than a selected threshold amount Δz gps ,thr, according to the independent estimate of relative altitude; (ii) the user determines that said true elevation z gps  (t) changes by no more than a selected threshold amount Δz gps ,thr ; (iii) the magnitude of the vertical component of velocity, |Δv vert ,gps |, estimated from GPS signals received from said GPS satellites, is no greater than a selected threshold Δv vert ,thr ; and (iv) the magnitude of the horizontal component of velocity, |Δv horiz ,gps |, estimated from GPS signals received from said GPS satellites, is no greater than a selected threshold Δv horiz ,thr.   
     
     
       11. The method of claim 7, wherein said step of providing a reference elevation coordinate z ref  (t) comprises the steps of: forming said difference between said altitude sensor reading and said reference elevation coordinate. C(t)=z alt  (t)-z ref  (t)=x +v1+v2, as a sum of a state vector x (t) representing the altitude sensor bias and two Statistical variables v1(t)=Q(t) and v2(t)=-G(t) that are independent, are approximately normally distributed, and have approximately zero statistical means;   selecting an initial estimate x 0  - of the state vector x  at a selected initial time t=t 0  and an initial uncertainty vector P 0  - that is equal to a number much larger than 1;   for each of a sequence of at least two times t=t k  >t O  (k=1, 2, . . . ), forming an altimeter bias term estimate C k  =C(t k ), a gain estimate K k , an updated state vector x k  and an estimate P k  of an error variance by the relations   K.sub.k =P.sub.k -/(P.sub.k -+R.sub.k),       x .sub.k =x .sub.k - +K.sub.k (C.sub.k -x .sub.k -)=(I-C.sub.k)x .sub.k - +K.sub.k C.sub.k,       P.sub.k =(I-K.sub.k)P.sub.k -;       computing a new estimate of the error variance   P.sub.k+1.sup.- =P.sub.k +D.sub.k,     where D k  is an estimate of the drift variance between two consecutive updates x  k  and x  k  of the state vector x;     identifying the value x  k  with an estimate of the altitude sensor bias B(t k ) at time t=t k  ; and   computing an estimate A est  (t cal ) for said true elevation coordinate at a selected location at a selected time t=t cal  ≈t k  by A est  (t cal )=z alt  (t cal )-x (t cal ).   
     
     
       12. The method of claim 7, further comprising the steps of: forming said difference between a reading of said altitude sensor and of said reference elevation coordinate, C(t)=z alt  (t)-z ref  (t)=B(t)+Q(t)-G(t), at each of a sequence of times t=t n  (n=1, 2, . . . );   computing a filtered value C f  (t) of said value C(t) at each of a sequence of times by the relation C f  (t n )=(1-K n )C(t n-1 )+K n  z alt  (t n ), where K n  =max and N max  is a selected positive integer;   computing said estimated altitude coordinate value A est  (t) at each of the sequence of times t for which t≧t Nmax  as a difference A est  (t)=z alt  (t)-C f  (t n ); and   replacing said location solution coordinate z gps  (t) by the value A est  (t) for at least one time t>t cal .   
     
     
       13. A method for determination of location coordinates of a selected position on or adjacent to the Earth's surface with improved accuracy, the method comprising the steps of: using a Global Positioning System (GPS) to determine the location coordinates (x gps , y gps , z gps ) of a selected location on or adjacent the Earth's surface, for GPS signals received from a group of GPS satellites numbered i=1, 2, . . . , N (N≧3), where the coordinate z gps  =z gps  (t) is an estimate of the true elevation or vertical coordinate A(t) of the selected location relative to a fixed vertical location at a selected time t;   providing an altimeter reading z alt  (t) that is an estimate of the elevation coordinate A(t) of the selected location relative to the fixed vertical location at a selected time t;   computing statistically determined estimates σ gps  (t) and σ alt  (t) of the standard deviations of the variables z gps  (t) and z alt  (t), respectively, for at least one selected time t;   defining an estimate A est  (t) of the elevation coordinate A(t) of the selected position to be equal to z gps  (t) if the standard deviations σ gps  (t) and σ alt  (t) satisfy a selected first criterion, and defining A est  (t) to be equal to z alt  (t) if the standard deviations σ gps  (t) and σ alt  (t) satisfy a selected second criterion, and defining A est  (t) to be equal to a value that lies between the value z gps  (t) and the value z alt  (t) if the standard deviations σ gps  (t) and σ alt  (t) satisfy neither the first criterion nor the second criterion, where the first criterion is σ gps  (t)<σ alt  (t)+Δz 1 , and the second criterion is σ gps  (t)>σ alt  (t)+Δz 2 , where Δz 1  and Δz 2  are selected real numbers that may be positive, negative or zero, with Δz 1  ≦Δz 2  ; and   calibrating the altimeter reading a alt  against an accurate value for z alt  at least once at a selected time t=t cal  subsequent to a time at which an altimeter reading is initially taken.   
     
     
       14. The method of claim 13, further comprising the step of calibrating said altimeter at said selected time t=t cal  by setting said coordinate z alt  (t cal )=z gps  (t=t cal ). 
     
     
       15. The method of claim 13, further comprising the step of calibrating said altimeter at said selected time t=t cal  by setting said coordinate z alt  (t cal ) equal to a trailhead value for said coordinate z alt . 
     
     
       16. A method for determination of location coordinates of a selected position on or adjacent to the Earth's surface with improved accuracy, the method comprising the steps of: using a Global Positioning System (GPS) to determine the location coordinates (x gps , y gps , z gps ) of a selected location on or adjacent to the Earth's surface, where the coordinate z gps  =z gps  (t) represents the true elevation or vertical coordinate A(t) of the selected location relative to a fixed elevation at a selected time t;   providing an altimeter having an altimeter reading z alt  (t) that is an estimate of the elevation coordinate A(t) of the selected location at a selected time t;   computing a statistically determined estimate σ gps  (t) of the standard deviation of the variable z gps  (t) for at least one selected time by the following steps:   computing the vertical dilution of precision VDOP(t) and the satellite pseudorange ρ i  (t) for each satellite number i in the satellite configuration used to determine the GPS location coordinates (x gps , y gps , z gps );   forming the product max i  [VDOP(t).ρ i  (t)]=ε V  (t) representing a statistical error variable for the pseudorange variables; and   defining said standard deviation σ gps  (t) to be the standard deviation σ.sub.εV (t) for the error variable ε V  (t);   computing a statistically determined estimate σ alt  (t) of the standard deviations of the variable z alt  (t) for the selected time t; and   estimating the elevation coordinate A(t) of the selected location by an estimated value A est  given by   A.sub.est (t)=w(t)z.sub.gps (t)+(1-w(t))z.sub.gps (t),     where w(t) is a weight function that tends monotonically toward the value 1 over a selected time interval, if the standard deviations σ gps  (t) and σ alt  (t) associated with the variables z gps  (t) and z alt  (t) satisfy a selected first criterion, and that tends monotonically toward the value 0 if the standard deviations σ gps  (t) and σ alt  (t) satisfy a selected second criterion.     
     
     
       17. The method of claim 16, further comprising the step of choosing said selected first criterion to be σ alt  (t)<ε V  (t)+Δz 1  and choosing said selected second criterion to be σ alt  (t)>ε V  (t)+Δz 2 , where Δz 1  and Δz 2  are selected real numbers that can be positive, negative or zero, with Δz 1  ≦Δz 2 . 
     
     
       18. A method for determination of location coordinates of a selected position on or adjacent to the Earth's surface with improved accuracy, the method comprising the steps of: using a Global Positioning System (GPS) to determine the location coordinates (x gps , y gps , z gps ) of a selected location on or adjacent the Earth's surface, for GPS signals received from a group of GPS satellites numbered i=1, 2, . . . , N (N≧3), where the coordinate z gps  =z gps  (t) is an estimate of the true elevation or vertical coordinate A(t) of the selected location relative to a fixed vertical location at a selected time t;   providing an altimeter reading z alt  (t) that is an estimate of the elevation coordinate A(t) of the selected location relative to the fixed vertical location at a selected time t;   computing a statistically determined estimate σ gps  (t) of the standard deviation of the variable z gps  (t) for at least one selected time by the following steps:   computing the vertical dilution of precision VDOP(t) and the satellite pseudorange ρ i  (t) for each satellite number i in the satellite configuration used to determine the GPS location coordinates (x gps , y gps , z gps );   forming the product max i  [VDOP(t).ρ i  (t)]=ε V  (t) representing a statistical error variable for the pseudorange variables; and   defining said standard deviation σ gps  (t) to be the standard deviation σ.sub.εV (t) for the error variable ε V  (t);   computing a statistically determined estimate σ alt  (t) of the standard deviations of the variable z alt  (t) for the selected time t; and   interpreting an estimate A est  (t) of the elevation coordinate A(t) of the selected position to be equal to z gps  (t) if the standard deviations σ gps  (t) and σ alt  (t) satisfy a selected first criterion, and defining A est  (t) to be equal to z alt  (t) if the standard deviations σ gps  (t) and σ alt  (t) satisfy a selected second criterion.   
     
     
       19. The method of claim 18, further comprising the step of choosing said selected first criterion to be σ alt  (t)<ε V  (t)+Δz 1  and choosing said selected second criterion to be σ alt  (t)>ε V  (t)+Δz 2 , where Δz 1  and Δz 2  are selected real numbers that can be positive, negative or zero, with Δz 1  <Δz 2 . 
     
     
       20. A method for determination of location coordinates of a selected position on or adjacent to the Earth's surface with improved accuracy, the method comprising the steps of: using a Global Positioning System (GPS) to determine the location coordinates (x gps , y gps , z gps ) of a selected location on or adjacent to the Earth's surface, where the coordinate z gps  =z gps  (t) represents the true elevation or vertical coordinate A(t) of the selected location relative to a fixed elevation at a selected time t;   providing an altimeter having an altimeter reading z alt  (t) that is an estimate of the elevation coordinate A(t) of the selected location at a selected time t;   computing statistically determined standard deviations σ gps  (t) and σ alt  (t) of the variables z gps  (t) and z alt  (t), respectively, for at least one selected time t;   estimating the elevation coordinate A(t) of the selected location by an estimated value A est  given by   A.sub.est (t)=w(t)z.sub.gps (t)+(1-w(t))z.sub.gps (t),     where w(t) is a weight function that tends monotonically toward the value 1 over a selected time interval, if the standard deviations σ gps  (t) and σ alt  (t) associated with the variables z gps  (t) and z alt  (t) satisfy a selected first criterion, and that tends monotonically toward the value 0 if the standard deviations σ gps  (t) and σ alt  (t) satisfy a selected second criterion, where the first criterion is σ gps  (t)<σ alt  (t)+Δz 1 , and the second criterion is σ gps  (t)>σ alt  (t)+Δz 2 , where Δz 1  and Δz 2  are selected real numbers that may be positive, negative or zero, with Δz 1  <Δz 2  ; and     calibrating the altimeter reading z alt  against an accurate value for z alt  at least once at a selected time t=t cal  subsequent to a time at which an altimeter reading is initially taken.   
     
     
       21. The method of claim 20, further comprising the step of calibrating said altimeter at said selected time t=t cal  by setting said coordinate z alt  (t cal )=z gps  (t=t cal ). 
     
     
       22. The method of claim 20, further comprising the step of calibrating said altimeter at said selected time t=t cal  by setting said coordinate z alt  (t cal  l ) equal to a trailhead value for said coordinate z alt . 
     
     
       23. A method for determination of location coordinates of a selected position on or adjacent to the Earth's surface with improved accuracy, the method comprising the steps of: using a Global Positioning System (GPS) to determine the location coordinates (x gps , y gps , z gps ) of a selected location on or adjacent the Earth's surface, for GPS signals received from a group of GPS satellites numbered i=1, 2, . . . , N (N≧3), where the coordinate z gps  =z gps  (t) is an estimate of the true elevation or vertical coordinate A(t) of the selected location relative to a fixed vertical location at a selected time t;   providing an altimeter having an altimeter reading z alt  (t) that is an estimate of the elevation coordinate A(t) of the selected location relative to the fixed vertical location at a selected time t;   computing statistically determined estimates σ gps  (t) and σ alt  (t) of the standard deviations of the variables z gps  (t) and z alt  (t), respectively, for at least one selected time t; and   defining the elevation coordinate A(t) of the selected location to be a linear combination of the values z gps  (t) and z alt  (t), defined by   z(t)=K.sub.1 z.sub.gps (t)+K.sub.2 z.sub.alt (t),       K.sub.1 =c.sub.1 (σ.sub.gps (t)).sup.p /[c.sub.1 (σ.sub.gps (t)).sup.p +c.sub.2 (σ.sub.alt (t)).sup.q ],       K.sub.2 =c.sub.2 (σ.sub.alt (t)).sup.q /[c.sub.1 (σ.sub.gps (t)).sup.p +c.sub.2 (σ.sub.alt (t)).sup.q ]=1-K.sub.1,     where C 1 , C 2 , p and q are selected positive constants.